The old Shogun clan was - in my opinion - a diluted clan. One that commited the same faults that large clans still make. Once a powerful clan with many warriors, people took a liking to the idea of being in one of the "big boy" clans and proceeded to apply en masse. Naturally, the quality of fighter within the clan eventually declined, as the clan became cumbersome under its own weight.
The only options for the clan was to either dissolve - as so many other large clans have done - or reorganize. They chose to reorganize and clean out the roster of warriors they deemed unworthy of bearing the name (MIA and incompetent fighters). They rallied under the new rule, and are now the Empire of the Romans (Basileia ton Romaion).
Red Lotus, led by (I believe) their lord Shogun Kimiko and their flagship fighter (imo) Sengo Muramasa aka Momento Mori are a vastly smaller clan albeit with very concentrated combat potential. They don't have much history beyond having named and blooded fighters from several different clans. Their combat skill, however, is solid albeit lacking the specific teamwork exemplified by other clans (the old Chaos pikers, Cavelier riders, ATS infantry and hoplites). I think that is simply because of the lack of diversity in their combat ranks. They mostly stay to katanas and nodachis, despite traditional Japanese combat (carried out with polearms, specifically naginatas and other hafted weapons).
In a straight up match between the old Shogunate vs Red Lotus: RL will take many Shogunate fighters down, but will eventually fall to combat attrition. If you're looking at mano-a-mano, RL will decimate most of the old Shogunate fighters, but perhaps not its top ranking warriors.
edit: If RL went clan to clan against the Byzantiums (reformed Shogun), they'd get positively steamrolled due to lack of weapon diversity.
edit2: Didn't vote because it's a pointless poll. You should change it to "Which clans dick would you suck" because it's really just a popularity contest, not any real assessment of combat potential.